Cluster Model Interrelation With Modern Physical Concepts by G. V. Kozlov

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By G. V. Kozlov

Fractal research supplies simply basic mathematical description of polymers, i.e. it doesn't establish structural devices (elements), from which any genuine polymer is shaped. actual description of thermodynamically non-equilibrium polymer constitution within the framework of the neighborhood order principles provides the cluster version of the polymer amorphous kingdom constitution that quantitatively determine its elements.Since those types think about the polymer constitution just a little from facets, they're very good finishing each other. it's common wisdom that constructions showing fractal behaviour on small size scale and being homogeneous on huge size scale are named homogeneous fractals. those fractals are percolation clusters on the percolation threshold. As proven lower than, the cluster constitution represents the percolation method and, as a result of the above-said, the homogeneous fractal. to place it another way, the presence of the neighborhood order within the condensed section of polymers determines fractality in their constructions.

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The same result was obtained for glassy polymer networks [68] and amorphous-crystalline polymers [114]. For example, in the framework of these general laws, the number of cross-link points, S, in a finite cluster, which can be the local order zone consisting of F/2 closely packed segments (where F is the cluster functionality [90]), depends upon dimensionless deviation of concentration, τ, from its critical value (τ = (х – хс)/хс [22]) at τ → 0 as follows: S~τ −γ n . (73) As mentioned above, the number of cross-link points, S, in the local order zone (classified as the cluster [34, 90]) equals F/2, and for τ parameter (Тg – Т)/Тg should be accepted.

The values of T0 and Т∞, obtained in this manner [125], are compared in Table 4. Figure 33. , for PC (1), PMMA (2) and HDPE (3) [9] Good conformity was obtained for all polymers, except for PC, for which calculation by the equation (42) gave physically meaningless ΔТ ≈ 670 K. The reason for this seeming non-correspondence is as follows. 5 is corresponded. e. in the state with higher local order degree, ϕcl) at a definite stage must be balanced by entropic chain straining forces. 58 G. V. Kozlov and G.

For chains with 0 T tetrahedral valence angle [60]. Thus substitution of d f or d f into equation (5) or (7) can help in the local order assessment, ϕ cl0 , maximum approachable for the current polymer, as the function of С∞ and S, the most important characteristics of the polymer. As temperature decreases below the point, at which ϕ cl0 is approached, the local order remains unchanged, so this temperature T0 can be assumed to be the analogue of Т∞, at which the polymer reaches constant free volume level [125].

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